My Mighty Mouse has never automatically connected. It's a favorite, and I've removed it and added it back. It still will not automatically connect when I turn it on. The Bluetooth keyboard automatically connects with no problem. At work, I connected an external screen for daily use, then took the MacBook Pro back home at the end of the day. It thus became very important to find a way to tell the computer to connect to the mouse with nothing more than the keyboard. The following is how you can connect to your mouse with nothing more than the keyboard if your arrangement is like mine.
First, navigate to the Bluetooth System Preferences panel. Make sure the last option (Show Bluetooth status in the menu bar) is enabled. That should put the Bluetooth icon in the right side of the menu bar. If I now press Control-F8, the system will select the far right menu bar option, which is my wireless connection. I then use the left arrow to get to the Bluetooth icon, then the down arrow to open its menu.
Since Browse Device... is closer to the bottom of the Bluetooth menu, I use the up arrow to start from the bottom, and hit it again until the Browse Device option is selected, and then I use the Enter key to select it. Listed under Device is my Mighty Mouse, so I use the down arrow until it is selected. Then I hit the Enter key so that it will try to search for available files on the mouse. Naturally it isn't able to browse and spouts an error message at the bottom,, but the result is that the mouse is now connected. Sometimes I have to repeat the selection of the mouse and hitting Enter to make it try to find files on the mouse for it to connect. Either way, this is much preferable to me over carrying a wired mouse around with me.
I have yet to see anybody give a real answer to solving the favorites issue with my Mighty Mouse, however. I hope this workaround helps others.
Mac OS X Hints